Specific physical conditioning is really important. After 20 years of experience of high altitude mountaineering, we can tell you that carrying a weighted backpack, building up the weight you carry, should be at the core of our training. We recommend building up to carrying double the weight you will carry on the mountain. Along with building up to maintaining an endurance based heart rate for 1 hour and 30 minutes in your daily training.
You should be aiming to build up hiking from 3 to 8 hours once a week. Hiking up and down hills is important, as this will be what you are doing on Kilimanjaro. You should be building from 500m/ 1,640 feet of elevation in a hike to 1,000m/ 3,280 feet in your weekend hike. Building slowly over months is important.
If you do not have access to hills, then you need to be using a stair master machine in the gym or stairs wherever you can find them. You are not running a marathon, you are hiking up and down the side of a big mountain, with weight on your back, all in a low oxygen environment. Some days are longer than others.
Your endurance training and leg strength are key components as you train for Kilimanjaro. We have no problem with you mixing up your training, however running should not be your core focus. You need to put on a weighted backpack, building up the weight you will carry and train 5 to 6 days a week. You can read our training advice on the linked page, however, we can tell you that the reasons most people fail to reach the summit is due to two factors; not enough days on the mountain and not doing the specific training that Kilimanjaro demands.